Finally something super interesting!

Statistical Modelling

A statistical model identifies of the distribution from which your data $\{x_1,x_2,\dots ,x_n\}$ is drawn.

• MAB algorithms builds up statistical models for each arm

For example, if we look at a data sample, and see that it looks like it follows a Normal Distribution, our our statistical model is $Y_i\sim N(\mu ,{\sigma }^2)$, but with $\mu ,{\sigma }^2$ unknown.

Notes

1. Attributes of the population that you are interested in are typically the parameters of your model
2. Finding a model is an empirical question, not theoretical

Once we can identify some sort of statistical model for our data, the goal is to estimate the parameters $\hat{\theta }(x_1,x_2,\dots ,x_n)$ of this statistical model. This process is called Estimation.